This trophy is glitched and I couldn't find any information online as to how to bypass the glitch, so, after discovering the solution it's about time to spread the word.
To earn this trophy you need to beat your previous best time on any challenge level however it will not unlock from that alone. You need to get a time on a level, ideally something you can beat and then EXIT the game completely (close application). Now when you reload the game go and beat your time and it will unlock.
Simply put, for some reason it won't count you beating your ghost unless you restart the game and then beat it.